Metamath Proof Explorer

Axiom ax-1

Description: AxiomSimp. Axiom A1 of Margaris p. 49. One of the 3 axioms of propositional calculus. The 3 axioms are also given as Definition 2.1 of Hamilton p. 28. This axiom is calledSimp or "the principle of simplification" inPrincipia Mathematica (Theorem *2.02 of WhiteheadRussell p. 100) because "it enables us to pass from the joint assertion of ph and ps to the assertion of ph simply". It is Proposition 1 of Frege1879 p. 26, its first axiom. (Contributed by NM, 30-Sep-1992)

Ref Expression
Assertion ax-1 φ ψ φ

Detailed syntax breakdown

Step Hyp Ref Expression
0 wph wff φ
1 wps wff ψ
2 1 0 wi wff ψ φ
3 0 2 wi wff φ ψ φ